This paper proposes an optimal rate allocation scheme for Fine-Granular Scalability (FGS) coded bitstreams that can achieve constant quality reconstruction of frames under a dynamic rate budget constraint. In doing so, we also aim to minimize the overall distortion at the same time. To achieve this, we propose a novel R-D labeling scheme to characterize the R-D relationship of the source coding process. Specifically, sets of R-D points are extracted during the encoding process and linear interpolation is used to estimate the actual R-D curve of the enhancement layer signal. The extracted R-D information is then used by an enhancement layer transcoder to determine the bits that should be allocated per frame. A sliding window based rate allocation method is proposed to realize constant quality among frames. This scheme is first considered for a single FGS coded source, then extended to operate on multiple sources. With the proposed scheme, the rate allocation can be performed in a single pass, hence the complexity is quite low. Experimental results confirm the effectiveness of the proposed scheme under static and dynamic bandwidth conditions.